1. What is the difference between consistent mass and lumped mass.

2. Write the consistent mass and lumped mass matrix formula for bar and beam elements.

3. Find the natural frequency of axial vibrations of a bar of uniform cross section of 40mm2 and of length 2.5 m. Take E=2.8 x 105 N/mm2 and density =7500 kg/m3. Take two liner elements.

4. Estimate the natural frequencies of axial vibration of a bar using both consistent and lumped mass matrices. The bar is of length of 1m made of the material having young’s modulus E= 2.5 x 1011 N/m2 and density =7800 kg/m3 . Use 2 element mesh. If exact solution is given by the relation

5. Solve the simultaneous equations given below using gauss elimination method.

6. Solve the simultaneous equations given below using gauss elimination method.

7. Solve the system of equations 3?1 − ?2 = −1, −?1 + 3?2 − ?3 = 7, −?2 + 3?3 = 7. Using
Cholesky decomposition method.

8. Solve the following system using LU decomposition method.

9. K and M matrix is given below. Find out natural frequencies using simultaneous iteration
method.

10. Solve the following system of equations by Crout's method. ?1 + ?2 + ?3 = 3,
2?1 − ?2 + 3?3 = 16 and 3?1 + ?2 − ?3 = −3.

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